Generalizing from a Few Examples

Yaqing WangQuanming YaoJames KwokLionel M. Ni

article2019ACM Computing Surveys2,192 citations

Establishes a unified taxonomy for few-shot learning by categorizing methods according to how prior knowledge is applied across data, model, and algorithm perspectives to overcome the core challenge of unreliable empirical risk minimization.

data-intensive application few-shot learning taxonomy Learning FSL Data

arXiv: 1904.05046

Paper: Optimization as a Model for Few-Shot Learning, S. Ravi et al. (2017). Reading this foundational meta-learning work on optimization-based few-shot adaptation provides the exact methodological grounding assumed by the source paper's taxonomy.
Paper: Prototypical Networks for Few-shot Learning, Jake Snell et al. (2017). Understanding prototypical networks is essential for grasping the metric-space and model-based few-shot learning strategies reviewed in the source.
Paper: Matching Networks for One Shot Learning, Oriol Vinyals et al. (2016). Reviewing matching networks clarifies how attention mechanisms over support sets solve few-shot tasks before reading the source's broader survey.
Paper: Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks, Chelsea Finn et al. (2017). MAML establishes the core gradient-based meta-learning paradigm that underpins much of the algorithmic taxonomy analyzed in the source.

Paper: Making Pre-trained Language Models Better Few-shot Learners, Tianyu Gao et al. (2021). This book chapter extends the source paper's few-shot principles into modern prompt-based fine-tuning methods for large language models.
Paper: Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning, Haokun Liu et al. (2022). Building directly upon few-shot learning foundations, this work explores parameter-efficient fine-tuning as a superior alternative to in-context learning.
Paper: Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing, Pengfei Liu et al. (2021). This comprehensive survey continues the few-shot narrative by examining how prompt-based methods replace traditional supervised training in language models.

Cover for Generalizing from a Few Examples

Abstract

Machine learning has been highly successful in data-intensive applications but is often hampered when the data set is small. Recently, Few-Shot Learning (FSL) is proposed to tackle this problem. Using prior knowledge, FSL can rapidly generalize to new tasks containing only a few samples with supervised information. In this paper, we conduct a thorough survey to fully understand FSL. Starting from a formal definition of FSL, we distinguish FSL from several relevant machine learning problems. We then point out that the core issue in FSL is that the empirical risk minimized is unreliable. Based on how prior knowledge can be used to handle this core issue, we categorize FSL methods from three perspectives: (i) data, which uses prior knowledge to augment the supervised experience; (ii) model, which uses prior knowledge to reduce the size of the hypothesis space; and (iii) algorithm, which uses prior knowledge to alter the search for the best hypothesis in the given hypothesis space. With this taxonomy, we review and discuss the pros and cons of each category. Promising directions, in the aspects of the FSL problem setups, techniques, applications and theories, are also proposed to provide insights for future research.

Topics

data-intensive application few-shot learning taxonomy

Keywords

Learning FSL Data Samples Few-Shot Conference Information Examples Dtrain Prior Knowledge

1 Introduction
1.1 Organization of the Survey
1.2 Notation and Terminology
2 Overview
2.1 Problem Definition
2.2 Relevant Learning Problems
2.3 Core Issue
2.3.1 Empirical Risk Minimization
2.3.2 Unreliable Empirical Risk Minimizer
2.4 Taxonomy
3 Data
3.1 Transforming Samples from Dtrain{D}_{\text{train}}
3.2 Transforming Samples from a Weakly Labeled or Unlabeled Data Set
3.3 Transforming Samples from Similar Data Sets
3.4 Discussion and Summary
4 Model
4.1 Multitask Learning
4.1.1 Parameter Sharing
4.1.2 Parameter Tying
4.2 Embedding Learning
4.2.1 Task-Specific Embedding Model
4.2.2 Task-Invariant Embedding Model
4.2.3 Hybrid Embedding Model
4.3 Learning with External Memory
4.3.1 Refining Representations
4.3.2 Refining Parameters
4.4 Generative Modeling
4.4.1 Decomposable Components
4.4.2 Groupwise Shared Prior
4.4.3 Parameters of Inference Networks
4.5 Discussion and Summary
5 Algorithm
5.1 Refining Existing Parameters
5.1.1 Fine-Tuning Existing Parameter by Regularization
5.1.2 Aggregating a Set of Parameters
5.1.3 Fine-Tuning Existing Parameter with New Parameters
5.2 Refining Meta-Learned Parameter
5.3 Learning the Optimizer
5.4 Discussion and Summary
6 Future Works
6.1 Problem Setups
6.2 Techniques
6.3 Applications
6.3.1 Computer Vision
6.3.2 Robotics
6.3.3 Natural Language Processing
6.3.4 Acoustic Signal Processing
6.3.5 Others
6.4 Theories
7 Conclusion
A Appendix: Meta-Learning
References

Knowls

Knowl 1 — Formal Definition of Few-Shot Learning
definition
In machine learning, a computer program is said to learn from experience $E$ with respect to a class of tasks $T$ and performance measure $P$ if its performance on $T$ , measured by $P$ , improves with $E$ .

Few-Shot Learning (FSL) is a type of machine learning problem (specified by $E$ , $T$ , and $P$ ) where the experience $E$ contains only a limited number of supervised examples directly relevant to the target task $T$ . In a standard supervised FSL task $T$ , the dataset $D = \{D_{\text{train}}, D_{\text{test}}\}$ consists of a small training set $D_{\text{train}} = \{(x_i, y_i)\}_{i=1}^I$ , where $I$ is small, and a test set $D_{\text{test}} = \{x^{\text{test}}\}$ .
- In $N$ -way- $K$ -shot classification, $D_{\text{train}}$ contains $I = K \times N$ labeled examples drawn from $N$ distinct classes, with exactly $K$ examples per class.
- When $K = 1$ , the task is termed one-shot learning.
- When $K = 0$ (meaning $E$ contains no supervised training examples of target classes), the problem becomes zero-shot learning (ZSL), which requires $E$ to include auxiliary information from other modalities (such as semantic attributes, WordNet hierarchies, knowledge graphs, or word embeddings) to enable cross-modal knowledge transfer.
Knowl 2 — Error Decomposition and the Core Issue of Few-Shot Learning
theoretical result
Let $p(x, y)$ denote the ground-truth joint probability distribution over input $x$ and output $y$ , $\ell(\hat{y}, y)$ denote a loss function measuring prediction error, and $\mathcal{H}$ denote a hypothesis space parameterized by $\theta$ . The expected risk $R(h)$ and empirical risk $R_I(h)$ evaluated on a training set $D_{\text{train}} = \{(x_i, y_i)\}_{i=1}^I$ of size $I$ are:

$R(h) = \mathbb{E}_{(x, y) \sim p}[\ell(h(x), y)], \qquad R_I(h) = \frac{1}{I} \sum_{i=1}^I \ell(h(x_i), y_i).$

Let $\hat{h} = \arg\min_h R(h)$ be the global optimal hypothesis, $h^* = \arg\min_{h \in \mathcal{H}} R(h)$ be the optimal hypothesis constrained within $\mathcal{H}$ , and $h_I = \arg\min_{h \in \mathcal{H}} R_I(h)$ be the empirical risk minimizer on $D_{\text{train}}$ . The total expected error decomposes into approximation error $\mathcal{E}_{\text{app}}(\mathcal{H})$ and estimation error $\mathcal{E}_{\text{est}}(\mathcal{H}, I)$ :

$\mathbb{E}[R(h_I) - R(\hat{h})] = \underbrace{\mathbb{E}[R(h^*) - R(\hat{h})]}_{\mathcal{E}_{\text{app}}(\mathcal{H})} + \underbrace{\mathbb{E}[R(h_I) - R(h^*)]}_{\mathcal{E}_{\text{est}}(\mathcal{H}, I)},$

where the expectation is taken over the random sampling of $D_{\text{train}}$ .

The core issue of FSL is that because the number of available supervised training samples $I$ is extremely small, the empirical risk $R_I(h)$ is a poor proxy for the expected risk $R(h)$ . Consequently, the empirical risk minimizer $h_I$ becomes unreliable and suffers from severe overfitting. To reduce total generalization error, FSL methods must leverage prior knowledge to augment data, constrain the complexity of $\mathcal{H}$ , or alter the algorithmic search for $h^*$ .
Knowl 3 — Three-Perspective Taxonomy for Few-Shot Learning
model/method
To address the unreliability of the empirical risk minimizer $h_I$ when the sample size $I$ is small, FSL methods incorporate prior knowledge across three distinct perspectives:
1. Data: Uses prior knowledge to augment the small training set $D_{\text{train}}$ , expanding its size from $I$ to $\tilde{I}$ where $\tilde{I} \gg I$ . Standard supervised learning models and optimization algorithms can then be directly applied to the augmented dataset to obtain a reliable empirical risk minimizer $h_{\tilde{I}}$ .
2. Model: Uses prior knowledge to constrain the capacity and structure of the hypothesis space $\mathcal{H}$ into a significantly smaller hypothesis space $\tilde{\mathcal{H}} \subset \mathcal{H}$ , removing hypotheses that are unlikely to contain the optimal $h^*$ . Within $\tilde{\mathcal{H}}$ , the small dataset $D_{\text{train}}$ contains sufficient supervision to identify a reliable empirical minimizer without overfitting.
3. Algorithm: Uses prior knowledge to guide or alter the parameter search strategy in $\mathcal{H}$ . Prior knowledge provides an informed parameter initialization $\theta_0$ or directly parameterizes a meta-learned optimizer that outputs update steps to find the optimal parameter vector $\theta^*$ for $h^*$ .
Knowl 4 — Data Augmentation Strategies for Few-Shot Learning
model/method
Data-perspective FSL methods use a transformer function $t(\cdot)$ informed by prior knowledge to synthesize additional samples $(\tilde{x}, \tilde{y})$ , expanding the training set $D_{\text{train}}$ via three primary data sources:
1. Transforming samples from $D_{\text{train}}$ : Learns transformation functions $t(x_i)$ from auxiliary classes (such as intra-class variation autoencoders, sample-pair difference transfer functions, or continuous attribute subspace regressors) and applies them to each $(x_i, y_i) \in D_{\text{train}}$ to generate $(t(x_i), y_i)$ .
2. Transforming samples from weakly labeled or unlabeled datasets: Employs a model pre-trained or refined on $D_{\text{train}}$ (e.g., exemplar SVMs, progressive pseudo-labeling, or label propagation on graph networks) to predict target labels $t(\bar{x})$ for unlabeled inputs $\bar{x}$ , augmenting $D_{\text{train}}$ with pseudo-labeled pairs $(\bar{x}, t(\bar{x}))$ .
3. Transforming samples from similar datasets: Aggregates and adapts labeled samples $\{(\hat{x}_j, \hat{y}_j)\}$ from related large-scale datasets using similarity metrics or dual-generator generative adversarial networks (GANs) that map between few-shot and abundant class domains, synthesizing $(t(\{\hat{x}_j\}), t(\{\hat{y}_j\}))$ .
A limitation of data augmentation strategies is that transformation policies are frequently hand-crafted or tailored in an ad-hoc manner for specific image datasets, making transfer to complex structural data (such as text or audio) non-trivial.
Knowl 5 — Hypothesis Space Constraining via Multitask Learning
model/method
Multitask learning constrains the few-shot hypothesis space by jointly learning $C$ related tasks $T_1, \dots, T_C$ with corresponding datasets $D_c = \{D^c_{\text{train}}, D^c_{\text{test}}\}$ , where few-shot tasks serve as target tasks and data-abundant tasks serve as source tasks. Joint learning forces the parameters $\theta_c$ of the task hypothesis $h_c$ to be constrained by information from other tasks via two main mechanisms:
- Parameter Sharing: Directly shares generic network layers (such as early convolutional feature extractors or variational autoencoder encoders) across all tasks, while training task-specific output layers or classification heads.
- Parameter Tying: Maintains separate parameter sets $\theta_c$ for each task while adding explicit regularization terms to the joint objective to penalize parameter divergences (e.g., pairwise distance penalties between parameter vectors $\|\theta_c - \theta_{c'}\|$ or layer-wise alignment terms).
A limitation of multitask learning in FSL is that all tasks must be trained jointly; introducing a new few-shot task requires retraining the full multitask model, and source tasks with large sample counts may dominate the optimization.
Knowl 6 — Hypothesis Space Constraining via Embedding Learning
model/method
Embedding learning projects input samples $x_i \in \mathcal{X} \subseteq \mathbb{R}^d$ into a lower-dimensional embedding space $z_i \in \mathcal{Z} \subseteq \mathbb{R}^m$ where intra-class samples cluster together and inter-class samples are well-separated, enabling the construction of a lower-complexity hypothesis space $\tilde{\mathcal{H}}$ .

The framework consists of an embedding function $f(x^{\text{test}})$ for test queries, an embedding function $g(x_i)$ for support samples $x_i \in D_{\text{train}}$ , and a similarity metric $s(f(x^{\text{test}}), g(x_i))$ . Methods fall into three categories:
1. Task-Specific Embedding: Learns embeddings using only task-specific sample pairs and ranking losses generated from $D_{\text{train}}$ .
2. Task-Invariant Embedding: Learns a fixed generic metric space across auxiliary tasks via episodic meta-learning without updating the embedding parameters on $D_{\text{train}}$ $D_{train}$ :
  - Matching Networks: Compares $f(x^{\text{test}})$ to each $g(x_i)$ using cosine similarity over contextual bidirectional LSTM representations.
  - Prototypical Networks (ProtoNet): Computes class prototypes $c_n = \frac{1}{K} \sum_{i=1}^K g(x_i)$ for each class $n$ and classifies $x^{\text{test}}$ using squared Euclidean distance: $s(f(x^{\text{test}}), c_n) = -\|f(x^{\text{test}}) - c_n\|_2^2$ .
  - Relation Networks / Graph Neural Networks: Parameterizes similarity metrics directly via deep neural networks or graph edge-update layers.
3. Hybrid Embedding: Dynamically adapts task-invariant embedding functions using task-specific embeddings extracted from $D_{\text{train}}$ (such as Learnet, TADAM, and dynamic conditional networks).
Knowl 7 — Hypothesis Space Constraining via External Memory Networks
model/method
External memory networks constrain the few-shot hypothesis space by storing knowledge extracted from $D_{\text{train}}$ into a key-value memory matrix $M \in \mathbb{R}^{b \times m}$ consisting of $b$ memory slots $M(i) = (M_{\text{key}}(i), M_{\text{value}}(i))$ . Test samples $x^{\text{test}}$ are represented as attention-weighted averages over retrieved memory values according to the similarity $s(f(x^{\text{test}}), M_{\text{key}}(i))$ .

Methods operate under two primary designs:
- Refining Representations: Stores support representations in memory (e.g., Memory-Augmented Neural Networks (MANN), surprise-based memory updating, and lifelong memory models). To protect rare/few-shot classes from being overwritten by abundant classes in lifelong settings, memory write operations reset the age of accessed slots to zero and selectively replace the oldest slot only when the predicted output is incorrect.
- Refining Parameters: Uses memory slots to store meta-learned "slow weights" and rapid task-specific "fast weights" (e.g., Meta Networks, conditionally shifted neurons) to modulate or generate network parameters conditioned on $D_{\text{train}}$ .
A limitation is the computational and memory footprint of matrix key-value lookups, which limits external memory sizes in practical deployments.
Knowl 8 — Hypothesis Space Constraining via Generative Modeling
model/method
Generative modeling methods constrain the hypothesis space $\mathcal{H}$ by modeling the data distribution $p(x; \theta) = \int p(x|z; \theta) p(z; \gamma) dz$ , where the latent prior distribution $p(z; \gamma)$ is pre-trained on auxiliary data to enforce structured inductive biases. The resulting posterior over latent parameters is constrained to a compact subspace $\tilde{\mathcal{H}}$ .

Generative FSL models are divided into three types:
1. Decomposable Components: Models objects hierarchically as combinations of shared primitive sub-parts (e.g., Bayesian Program Learning decomposes handwritten characters into types, tokens, templates, parts, and strokes), restricting inference to valid component combinations.
2. Groupwise Shared Priors: Discovers hierarchical task clusters via unsupervised learning on auxiliary datasets $\{D_c\}$ to learn group-level class prior probabilities, which are inherited by novel few-shot classes assigned to that cluster.
3. Inference Networks: Approximates intractable true posteriors $p(z|x; \theta, \gamma) = \frac{p(x|z; \theta)p(z; \gamma)}{\int p(x|z; \theta)p(z; \gamma)dz}$ via amortized variational inference using deep inference networks $q(z; \delta)$ (e.g., variational autoencoders, conditional autoregressive models, GANs).
A limitation is that generative inference involves higher computational cost and more complex derivation compared to deterministic discriminative models.
Knowl 9 — Search Strategy Alteration via Pre-trained Parameter Refining
model/method
This strategy uses an initial parameter vector $\theta_0$ pre-trained on related tasks to provide a favorable starting point in the hypothesis space $\mathcal{H}$ , reducing the required optimization steps on the small target dataset $D_{\text{train}}$ . To prevent severe overfitting during standard gradient descent on $D_{\text{train}}$ , several regularization techniques are employed:
- Fine-Tuning by Regularization: Prevents overfitting via early stopping on a split validation subset, selective updating (freezing most pre-trained layers and updating only specific filter strengths or top layers), grouping related weights (updating neuron clusters jointly), or learning a model regression network that maps few-shot parameter estimates to large-sample parameter values.
- Aggregating Pre-trained Parameters: Reuses and combines multiple pre-trained model parameter vectors $\{\theta_0^k\}$ learned from diverse auxiliary tasks by learning linear combination coefficients on $D_{\text{train}}$ .
- Parameter Expansion: Preserves pre-trained feature parameters $\theta_0$ and introduces dedicated task-specific parameters $\delta$ (e.g., learning a linear classifier head on fixed deep features, $\theta = \{\theta_0, \delta\}$ ).
A trade-off of pre-trained parameter refining is that $\theta_0$ is static and learned from disparate tasks, which can sacrifice task-specific precision for optimization speed.
Knowl 10 — Search Strategy Alteration via Meta-Learned Parameter Initialization
model/method
Meta-learned parameter initialization optimizes an initial parameter vector $\theta_0$ across a distribution of training tasks $p(T)$ such that one or a few gradient descent steps on few-shot data $D^s_{\text{train}}$ yield high generalization performance on $D^s_{\text{test}}$ .

In the Model-Agnostic Meta-Learning (MAML) framework, given task $T_s \sim p(T)$ , task adaptation is performed in an inner loop via gradient descent:

$\phi_s = \theta_0 - \alpha \nabla_{\theta_0} \mathcal{L}^s_{\text{train}}(\theta_0),$

where $\alpha$ is the inner step size and $\mathcal{L}^s_{\text{train}}$ is the empirical loss on $D^s_{\text{train}}$ . Across meta-training tasks, the meta-parameter $\theta_0$ is optimized in an outer loop via feedback on test sets $D^s_{\text{test}}$ :

$\theta_0 \leftarrow \theta_0 - \beta \nabla_{\theta_0} \sum_{T_s \sim p(T)} \mathcal{L}^s_{\text{test}}(\phi_s),$

where $\beta$ is the meta-step size.

Key extensions to MAML include:
1. Conditioning initialization on task-specific subspaces or embeddings to avoid uniform initializations across heterogeneous tasks.
2. Probabilistic and hierarchical Bayesian formulations to model epistemic parameter uncertainty resulting from tiny sample sizes.
3. Regularizing inner gradient descent trajectories using model regression networks.
Knowl 11 — Search Strategy Alteration via Learned Optimizers
model/method
Instead of using hand-designed gradient descent update rules to search the parameter space $\mathcal{H}$ , learned optimizer methods meta-learn an optimization model (such as a Recurrent Neural Network or LSTM) that directly computes and outputs parameter update steps $\Delta\phi_t$ .

At iteration $t$ of learning a new task, the task-specific parameter $\phi_t$ is updated as:

$\phi_t = \phi_{t-1} + \Delta\phi_{t-1},$

where the meta-learner receives the loss signal $\ell_t(\phi_{t-1}) = \ell(h(x_t; \phi_{t-1}), y_t)$ and gradient information from the learner on support sample $(x_t, y_t) \in D_{\text{train}}$ , and produces $\Delta\phi_{t-1}$ directly. In LSTM-based optimizers, the learner's parameter $\phi_t$ is mapped directly to the cell state of the LSTM meta-learner.

The meta-optimizer's own parameters are optimized across tasks $T_s \sim p(T)$ using gradient descent on test loss $\mathcal{L}^s_{\text{test}}(\phi_T)$ evaluated on $D^s_{\text{test}}$ , eliminating manual tuning of step sizes and search directions.
Knowl 12 — Episodic Meta-Learning Framework for Few-Shot Learning
definition
Meta-learning for few-shot learning operates over a task distribution $p(T)$ using an episodic training and evaluation paradigm partitioned into meta-training and meta-testing phases:
- Meta-Training: Samples a set of support tasks $T_s \sim p(T)$ . Each task $T_s$ provides an episode dataset $D_s = \{D^s_{\text{train}}, D^s_{\text{test}}\}$ with $N$ classes, where $D^s_{\text{train}}$ contains $K$ examples per class ( $N$ -way $K$ -shot). The meta-learner optimizes generic meta-parameters $\theta_0$ across tasks to minimize the expected test loss across learners:
$\theta_0 = \arg\min_{\theta_0} \mathbb{E}_{T_s \sim p(T)} \sum_{(x_i, y_i) \in D^s_{\text{test}}} \ell(h(x_i; \theta_0(D^s_{\text{train}})), y_i).$
- Meta-Testing: Evaluates generalization using a disjoint set of test tasks $T_t \sim p(T)$ with datasets $D_t = \{D^t_{\text{train}}, D^t_{\text{test}}\}$ drawn from target classes unseen during meta-training. The learner adapts using $D^t_{\text{train}}$ and is evaluated on $D^t_{\text{test}}$ , with the average loss across all $T_t$ defining the meta-learning test performance.

Coverage note — Domain-specific benchmark applications (e.g., character recognition on Omniglot, image classification on miniImageNet, robotics, and NLP benchmarks) and citations of individual application papers were omitted as they exemplify application instances rather than the survey's foundational contributions (the formal problem definitions, error analysis, three-perspective taxonomy, and category-level methodological mechanisms).

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MLA

Wang, Y., et al. “Generalizing from a Few Examples: A Survey on Few-Shot Learning”. arXiv, 2019, http://arxiv.org/abs/1904.05046v3.

APA

Wang, Y., Yao, Q., Kwok, J., & Ni, L. M. (2019). Generalizing from a Few Examples: A Survey on Few-Shot Learning. arXiv. http://arxiv.org/abs/1904.05046v3

Chicago

Wang, Y., Q. Yao, J. Kwok, and L. M. Ni. 2019. “Generalizing from a Few Examples: A Survey on Few-Shot Learning”. arXiv. http://arxiv.org/abs/1904.05046v3.

Harvard

Wang, Y. et al. (2019) “Generalizing from a Few Examples: A Survey on Few-Shot Learning”, arXiv [Preprint]. Available at: http://arxiv.org/abs/1904.05046v3.

Vancouver

1. Wang Y, Yao Q, Kwok J, Ni LM (2019) Generalizing from a Few Examples: A Survey on Few-Shot Learning. arXiv

BibTeX

@article{wang2019generalizing,
  title = {Generalizing from a Few Examples: A Survey on Few-Shot Learning},
  author = {Wang, Yaqing and Yao, Quanming and Kwok, James and Ni, Lionel M.},
  year = {2019},
  journal = {arXiv},
  url = {http://arxiv.org/abs/1904.05046v3},
  eprint = {1904.05046}
}

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Generalizing from a Few Examples

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Knowls

Knowl 1 — Formal Definition of Few-Shot Learning

Knowl 2 — Error Decomposition and the Core Issue of Few-Shot Learning

Knowl 3 — Three-Perspective Taxonomy for Few-Shot Learning

Knowl 4 — Data Augmentation Strategies for Few-Shot Learning

Knowl 5 — Hypothesis Space Constraining via Multitask Learning

Knowl 6 — Hypothesis Space Constraining via Embedding Learning

Knowl 7 — Hypothesis Space Constraining via External Memory Networks

Knowl 8 — Hypothesis Space Constraining via Generative Modeling

Knowl 9 — Search Strategy Alteration via Pre-trained Parameter Refining

Knowl 10 — Search Strategy Alteration via Meta-Learned Parameter Initialization

Knowl 11 — Search Strategy Alteration via Learned Optimizers

Knowl 12 — Episodic Meta-Learning Framework for Few-Shot Learning

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